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Some bullfrogs were introduced into a small pond. The graph shows the bullfrog population for the next few years. Assume that the population grows exponentially.

equation: 140(315/140)^(t/2)
What is the growth rate?

Respuesta :

scme1702
For exponential growths,
population after time t = original population x (growth rate)^time
The growth rate works out to be:
(315/140)^(t/2)
= [√(315/140)]^t
= 1.5^t
The growth rate is 1.5 times per year.
InesWalston

Answer:

50%

Step-by-step explanation:

The general exponential growth function is,

[tex]y(t)=a(1+r)^t[/tex]

where,

y(t) is the function of time t, which represents the future amount,

a = initial amount,

r = growth rate in decimals,

The given function is,

[tex]=140\left(\dfrac{315}{140}\right)^{\frac{t}{2}}[/tex]

[tex]=140\left(\dfrac{315}{140}\right)^{\frac{1}{2}\cdot t}[/tex]

[tex]=140\left(\left(\dfrac{315}{140}\right)^{\frac{1}{2}\right)^t}[/tex]

[tex]=140\left(\sqrt\dfrac{315}{140}\right)^t}[/tex]

[tex]=140(1.50)^{t}[/tex]

[tex]=140(1+0.50)^{t}[/tex]

Comparing this with the general function, we get the growth rate as 0.50 or 50%